Elimination Method Calculator

The elimination method—also known as addition or subtraction method—is a standard algebraic technique used to solve systems of two linear equations in two variables. Standard form is represented as A1x + B1y = C1 and A2x + B2y = C2. The core objective is to multiply one or both equations by specific constants so that the coefficients of either x or y become exact opposites. When you add the two modified equations together, the targeted variable cancels out (gets eliminated), leaving a single-variable equation that is easily solved. Once that first variable value is found, it is substituted back into either original equation to solve for the remaining variable.

Consider the following system of linear equations: Equation 1 is 2x + 3y = 12, and Equation 2 is 4x - y = 5. To eliminate the y variable, we can multiply Equation 2 by 3, which transforms it into 12x - 3y = 15. Now, add this new equation to Equation 1: (2x + 12x) + (3y - 3y) = 12 + 15. This simplifies to 14x = 27, meaning x = 27/14 (approximately 1.928). Substituting this x value back into the original second equation gives 4(1.928) - y = 5, which reveals that y = 2.714. Our calculator automates these scaling and addition steps instantly for any valid inputs.

When setting up your equations, ensure both are in strict standard form (Ax + By = C) before inputting values. Watch out for negative signs, as missing a negative coefficient is the most common cause of calculation errors. If your system yields parallel lines with no intersection, the calculator will flag inconsistent parameters because an elimination solution does not exist.